# ﻿Interpreting Graphs of Proportional Relationships

Warmup

4 seagulls ate 10 pounds of garbage. Assume this information describes a proportional relationship. Plot a point that shows the number of seagulls and the amount of garbage they ate. Then use the tools to draw a line through your point and (0,0).

Plot the point (1, k) on the line in the app above. What is the value of  K ? What does the value of  k tell you about this context?

Activity #1

Interpret Graphs of Proportional Relationships.

Tyler was at the amusement park. He walked at a steady pace from the ticket booth to the bumper cars.

• Use the graph to answer the questions below.

(1.) The point on the graph shows his arrival at the bumper cars. What do the coordinates of the point tell us about the situation?

The table on the left of the graph representing Tyler’s walk shows other values of time and distance.

• Complete the table.
• Next, plot the pairs of values on the grid.

(2.) What does the point (0,0) mean in this situation?

(3.) How far away from the ticket booth was Tyler after 1 second?

• Label the point on the graph that shows this information with its coordinates.

(3.) What is the constant of proportionality for the relationship between time and distance?

(4.) What does it tell you about Tyler’s walk?

(5.) Where do you see it in the graph?

(6.) If Tyler wanted to get to the bumper cars in half the time, how would the graph representing his walk change?

(7.) How would the table change?

(8.) What about the constant of proportionality?

Activity #2

Interpret More Graphs of Proportional Relationships.

There is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. The cost for 6 months is \$47.94. The point (6, 47.94) is shown on the graph.

• Examine the graph carefully and answer the questions that follow.

(1.) What is the constant of proportionality in this relationship?

(2.) What does the constant of proportionality tell us about the situation?

(3.) Add at least three more points to the graph and label them with their coordinates.

(4.) Write an equation that represents the relationship between  C, the total cost of the subscription, and , m the number of months.

Activity #3

Solve Proportional Relationships on a Graph..

Here is a graph that represents a proportional relationship.

• Give the graph a title, and then label the axes with the quantities in your situation.

There is a point that is marked on the graph. What are its coordinates? What does it represent in your situation?

Challenge #1

To make a friendship bracelet, some long strings are lined up then taking one string and tying it in a knot with each of the other strings to create a row of knots. A new string is chosen and knotted with the all the other strings to create a second row. This process is repeated until there are enough rows to make a bracelet to fit around your friend’s wrist.

(1). Are the number of knots proportional to the number of rows? Explain your reasoning.

(2). What information do you need to know to write an equation relating two quantities that have a proportional relationship?

Challenge #2

Here is a graph that represents a proportional relationship.

Invent a situation that could be represented by this graph.

Challenge #3

The graph shows the amounts of almonds, in grams, for different amounts of oats, in cups, in a granola mix.

Label the point on the graph by dragging the red point, find the value of , and explain its meaning.

Quiz Time